- #1

oldman

- 633

- 5

*The Mysterious Universe*I came across his statement that "the capacity for tying knots is limited to space of three dimensions", in the context of sailor's knots. I'm no mathematician, but understand that mathematical folk regard a knot more generally as a topological feature of an n-dimensional closed loop "embedded in" an m (>n+2)-dimensional space.

May I ask why the 2?

Seems reasonable to me for ropes in the space we live in. Ropes are like 1-dimensional lines that need one extra dimension to be loops in and another extra dimension to be crossed in to make knots. Makes a total of 1+2 = 3 needed dimensions. Does having more dimensions than 3 for ropes simply mean that the crossings can then be removed by using yet other dimension(s) to undo crossings without cutting the loop or passing the rope through itself? Or is this too simple minded?

Somebody must somewhere have suggested that knotted loops, perhaps unrecognised as such, might be enduring features in the three dimensions of the spacetime we inhabit. Probably in Maxwell's time.